"What does width and length refer to?"
Width refers to front to back and length refers to side to side.

"What do the different types of stainless steel (304, 316, etc) mean?"
The term "stainless steel" refers to specific grades of steel that contain more than 10% chromium. Stainless steel may also include a variety of other elements (such as nickel, titanium, molybdenum, etc); it resists corrosion and is generally a stronger, more reliable steel. The most common grades of stainless steel are:

Type 304: Aside from having a higher content of chromium than most other types of stainless steel, type 304 also contains nickel; this enables it to withstand most ordinary corrosion in architecture, is durable in typical food processing environments, and resists most chemicals.

Type 316: Similar to type 304, but also contains a small amount of molybdenum, which is an alloy element #304 does not contain (but one that provides even stronger resistance to some deterioration). Types 304 and 316 are grades of stainless steel that are most often used in plumbing, as well as in the manufacturing of kitchen utensils and sinks.

Type 409: Does not contain virtually any nickel at all, but also is the stainless steel that contains the least amount of chromium. Type 409 is more suitable for high temperature applications, which is why it's often used in automotive trim and exhaust systems, or hot water tanks.

Type 410: Also does not contain any significant nickel; its primary difference to type 409 stainless is characterized by the use of heat treatment for hardening and strengthening. Type 410 is not appropriate for severely corrosive applications, but used instead in environments that require high strength; this is why it's the type of stainless steel that's often used in surgical equipment.

Type 430: Another plain-chromium stainless steel, similar to type 409, but is usually used in decorative applications.